Derivative of the exponential map

The exponential map is a fundamental concept in differential geometry, particularly in the context of Riemannian manifolds and Lie groups. In general, the exponential map takes a tangent vector at a point on a manifold and maps it to a point on the manifold itself. ### Derivative of the Exponential Map The derivative of the exponential map has different forms depending on the context (e.g., Riemannian geometry or Lie groups).